Shaft having axial pre-stress

ABSTRACT

A shaft, having a length and two ends, a handle end and an opposite end, is arranged to have two or more concentric, longitudinal members in at least along a major portion of its length; when a lateral load acts at the opposite end, the shaft bends in the conventional primary bending mode of a cantilever beam; the structural members of the shaft is characterized by said concentric members having a substantial, permanent axial pre-stress, wherein each member is either in compression or in tension, constitutes an internal self equilibrating force system.

BACKGROUND OF THE INVENTION

[0001] The present invention concerns a new shaft, in which the bendingstiffness of the shaft is controlled by a pre-stress in the shaft, whichis readily adjustable.

[0002] A golf club shaft is described in detail as an example. Thechoice of bending stiffness of golf shaft is limited, which is fixed inthe factory. From the most stiff to the most soft, there are only fivestiffness grades, being offered to the public.

[0003] For metal wood clubs of a standard length, the softest L gradeshaft deflects about 210 mm and the stiffest XS grade deflects 135 mm,which is a 36% difference. At present there is no golf club shaft whosestiffness can be adjusted.

[0004] In theory of mechanics, it is known that the end deflection of acantilever beam under end load is changed when it has a simultaneousinternal axial force. It is because under the simultaneous loading, theneutral axis of the beam is no longer at its mid-plane. It is shifted upor down, so that the total potential of the shaft is a minimum.

[0005] A shaft can be made stiffer in bending by having a tensilepre-stress, and less stiff by a compressive pre-stress. A difficulty ofapplication of the invention is in the arrangement of the pre-stress andthe lacking of a way to estimate the changed stiffness.

[0006] The invention suggests a self-equilibrating internal forcesystem, establishes rules governing the design and a simple procedure toestimate the changed bending stiffness.

[0007] The invention has applications besides golf club shaft. It can beused in other kind of shafts, such as fishing rods, instrument parts,machine parts, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008]FIG. 1 shows the Table 9a, Reaction and Deflection coefficientsfor beams under simultaneous loading, taken from p. 157, Roark'sFormulas for Stress & Strain, by Warren C. Young, sixth Edition,McGraw-Hill, Inc.

[0009]FIG. 2A shows a cantilever beam having an end load W, and adeflection denoted as d. The deflection is reduced to d* with asimultaneous axial tension force P.

[0010]FIG. 2B curve A plots the Force and Rigidity Coefficient of apre-tensioned beam versus the Deflection Reduction, d*/d, based on FIG.1 table data. Curve B is the force P versus d*/d of the pre-stressedshaft shown in FIG. 3.

[0011]FIG. 3 shows a golf club shaft its inner member is in compression

[0012]FIG. 4 shows a golf club shaft its inner member is in tension.

A PRINCIPLE TO ARRANGE THE PRE-STRESS

[0013] The principle of the design of a pre-stressed shaft is asfollows:

[0014] (1), The shaft includes concentric, longitudinal structuralmembers, the majority of them joined at their two ends. The majority ofmembers are pre-stressed permanently, in tension or in compressionrespectively, at least along a significant part of their length. Thepart of the member, which carries pre-stress, does not enter into thepart of the body, which does not participate in the bending process,such as the head part of the club.

[0015] (2), If the adjustment of the axial force is either increasing ordecreasing, and if the shaft deflection is to be reduced with increasingpre-stress, the sum of the bending rigidity of its tension membersshould be significantly greater than that of the compression members;and if the shaft deflection is to be increased with increasingpre-stress, the sum of the bending rigidity of its compression membersshould be significantly greater than that of the tension members.

[0016] (3), The internal axial force is substantial, and isself-equilibrating.

A GOLF CLUB SHAFT EMBODIMENT

[0017]FIG. 3 is the embodiment of a golf club shaft 1, having a lengthL, and two ends: a handle end 2 and an opposite end 3, which leads tothe golf club head. The golf shaft consists of a cylindrical outermember 4 and an inner member 5. The two members as shown have a threadedjoint 7 at the handle end and a fixed joint at the opposite end 6. Whenthe smaller inner member is being pushed down from the grip end, joint 6will pull the outer member with an equal force P. It is to be noted thatthe structural end of the shaft at end 2 may be extended beyond 2. Theend point 2 and the length L begins where the force engagement of thetwo members actually begins, which is the length that counts in theinvention. In this embodiment the outer member has the predominatebending rigidity. Such an internal force system is a self-equilibratingsystem. If the applied force P is to be adjustable, a screw and threaddevice such as 7, which engages 4 to 5 at the handle end 2, may be used.A screwdriver is sufficient to adjust the force P from the outsidethrough a small recoverable opening made at 2.

[0018] To maintain a constant force, a spring device 8 is optional. Theinterfaces between contacting members may be free, may have cushions; orfixed, such as by adhesives.

[0019] In FIG. 3, the bending stiffness of the shaft is increased by theaxial tension of the outer member through the compressed inner member.For the case of a shaft to be softened by the pre-stress, the innermember is in tension, and the outer member is in compression. The innermember may be a wire-like structural element or a small bar as shown inFIG. 4. Other configurations may have more than two members. In general,some members may be only partially stressed, or not stressed at all, orits length may be shorter than full.

NUMERICAL EXAMPLE

[0020] The following lists geometry and physical data of the FIG. 3carbon-fiber golf shaft:

[0021] Shaft length L=107 cm. Outside diameter=1.30 cm. Insidediameter.=1.00 cm.

[0022] 10-ply wall thickness=0.15 cm. Vol.=58 cc. Shaft weight=67.0 g.

[0023] Material density=1.15 g per c.c. Young's modulus E=1,310,000kg/sq.cm.

[0024] The bending rigidity EI of the shaft is 119,200 kg-sq.cm, where Eis the material's Young's modulus and I its sectional moment of inertia.Assume the outer member has 6 plies, which is 69% of the EI, and theinner has 4, which is 31%. Without the axial force, the members sharethe bending load W at the ratio of 69% to 31%, as the ratio of theirrespective bending stiffness. With axial force, the load ratio changesmore to the stiffer.

SHAFT STIFFNING THROUGH AXIMAL PRE-STRESS

[0025] Assume the inner member is able to sustain the axial compressiveforce P and its Deflection Ratio d*/d remains a constant 1.67 as shownin FIG. 1 table. An equation that the deflections of the two ends areequal yields Eq. (1), where X is the percentage of the load on thetension member:

X=1.0/[1.0+(C×D)],   (1)

[0026] where

[0027] C=ratio of d*/d of the tension member to d*/d of the compressionmember,

[0028] D=ratio of the compression member's EI to the tension member'sEI.

[0029] The same equation also gives the final deflection ratio d*/d ofthe shaft, denoted as R,

R=1.0/[(U/V)+(1−U)/H],   (2)

[0030] where

[0031] U=ratio of EI of the tension member to the EI of the total shaft.

[0032] V=d*/d of the tension member under the axial tension force P.

[0033] H=d*/d of the compressed member under the axial compressive forceP.

[0034] As an example, assume the axial force P is 10 kg. We getC=0.65/1.67, D=0.31/0.69, U=0.69, V=0.65, and H is taken from the FIG. 1compression table as 1.67.

[0035] From Eq. (1) and (2), the load ratio X is 0.85 and the shaftdeflection ratio R is 0.80.

[0036] Compute for more P points, one gets the Curve B of FIG. 2B. Itshows the stiffening effect obtained if the sample shaft of FIG. 3 has 6plies for the outer member and 4 plies for the inner member. The resultshows at an axial compression force of 19 kg (42 lb), the deflectionratio d*/d reaches 0.64. This corresponds to a 36% deflection reduction,the full range of stiffness change. This point is marked in FIG. 2Bcurve B. If the base shaft begins as a soft grade L shaft, the 36%deflection reduction makes the shaft to become the stiffest XS shaft. Aplayer can adjust the stiffness by a screwdriver to get any stiffnesswithin that 36% range.

SHAFT SOFTENING THROUGH PRE-STRESS

[0037] An analysis is done also for the case of having a compressedouter member with a tensioned inner member as shown in FIG. 4. In thisarrangement, the inner member is a wire-like structural element and theouter member is structurally the main shaft, which takes the full load.The advantage is that the inner member's rigidity and weight are almostnegligible.

[0038] To get the fill range of deflection reduction 36% between the XSstiff state to the final L state, the desired d*/d ratio is 1.56, whichyields the Force & Rigidity Coef. of 0.94 from the FIG. 1 compressiondata. The required P to yield the Coef of 0.94 is found as 9.30 kg (20lb). The analysis is simple, because the outer member is practically thecomplete shaft. This greatly simplifies the analysis.

[0039] The base shaft may begin as a stiff shaft, XS, and then the axialforce in the inner element is increased as intended to control thestiffness of the shaft.

COMMENT

[0040] As seen from the data presented in FIG. 1 tables and FIG. 2Bcurves that, for the pre-stress begins to have noticeable and meaningfulbending stiffening or softening effect on a shaft device, especially asapplied to golf club shaft with comparable bending rigidities as givenin the sample problem, it is reasonable to suggest that:

[0041] For bending stiffness increment of the shaft device which derivesfrom the tensioned outer member, the axial compression force applied tothe inner member may begin at approximately 4.0 kg (8.8 lb) and upward,and the Deflection Reduction Coef. d*/d of the shaft may begin from0.94; and

[0042] For bending stiffness reduction of the shaft device which derivesfrom the compression outer member, the axial tension force applied tothe inner member may begin at approximately 2.0 kg (4.4 lb) and upward,and the Deflection Reduction Coef. d*/d of the shaft may begin from1.10.

[0043] Finally, one may suggest that for the bending stiffness reductionmode mentioned above, a conversion kit may be adapted to be incorporatedinto a hollow shaft device, such as a golf club, for controlling thedeflection when the shaft is under a bending load. The kit comprises atleast a wire-like elongated, structural element and means for connectingthe structural element to the ends of the hollow shaft device andproducing adjustable stresses to control the bending of the shaftdevice.

What is claimed is:
 1. A shaft device having a handle end and anopposite end, comprising at least two or more concentric, longitudinalmembers in at least along a major portion of its length, and beingadapted to deflect, in the primary conventional bending mode of acantilever beam; when a transverse load acts against said opposite endwhile holding said handle end immobile, said concentric members having asubstantial, permanent axial pre-stress in either compression or intension, thereby constituting an internal self-equilibrating forcesystem.
 2. The shaft device as defined in claim 1 wherein each of saidmembers has its own bending rigidity, and is arranged wherein the sum ofthe bending rigidities of all tension members is greater than the sum ofthe bending rigidities of the compression members.
 3. The shaft deviceas defined in claim 1 wherein each of said members has its own bendingrigidity, and it is arranged wherein the sum of the bending rigiditiesof all compression members is greater than the sum of the bendingrigidities of the tension members.
 4. The shaft device as defied inclaim 2 being adapted whereby said end deflection of the shaft deviceunder a transverse end load will be decreased as compared to the shaftdevice under the same load but with internal pre-stress removed, andsaid end deflection will further decrease when the pre-stress in saidmembers is further increased.
 5. The shaft device as defined in claim 3being adapted whereby said end deflection of the shaft device under atransverse end load will be increased as compared to the shaft deviceunder the same load but with internal pre-stress removed, and said enddeflection will further increase when the pre-stress in said members isfurther increased.
 6. The shaft device as defined in claim 1 wherein theshaft device has two concentric members.
 7. The shaft device as definedin claim 1 wherein the shaft device is a golf club shaft.
 8. The shaftdevice as defined in claim 1 including a screw device arranged in saidhandle end being adapted for producing said axial force system.
 9. Theshaft device as defined in claim 1 including a spring device arranged insaid handle end for maintaining said axial force constant.
 10. The shaftdevice as defined in claim 1 wherein said concentric members have aninterface therebetween which has a portion partly fixed whereby saidmembers can not slide relative to each other after internal stresses arepermanently established.
 11. The shaft device as defined in claim 5wherein the innermost member is a thin wire-like structural element heldin tension thereby subjecting the outermost member in compression.
 12. Aconversion kit adapted to be incorporated into a hollow shaft device,such as a golf club, for controlling the flexing thereof when the sameis deflected at one end during swinging of the shaft device, comprisinga wire-like elongated, structural element connected adjacent its spacedends to spaced points within and along the shaft device, means forproducing tension on said structural element thereby producingcompression in the shaft device between said points of connection. 13.The conversion kit as defined in claim 12 including means positioned atone of said ends of said structural element for adjusting said tensionon said structural element and thereby adjusting said compressionaccordingly.
 14. The shaft device as defined in claim 1 wherein at leastone or more of said members may not be pre-stressed, or pre-stressedonly partially along its length, or its length is less than the fulllength from said handle end to said opposite end.